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Identification and Use of Efficient Faces and Facets in DEA

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  • Ole Olesen

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  • N. Petersen

    ()

Abstract

This paper provides an outline of possible uses of complete information on the facial structure of a polyhedral empirical production possibility set obtained by DEA. It is argued that an identification of all facets can be used for a characterization of basic properties of the empirical production frontier. Focus is on the use of this type of information for (i) the specification of constraints on the virtual multipliers in a cone-ratio model, (ii) a characterization of the data generation process for the underlying observed data set, and (iii) the estimation of isoquants and relevant elasticities of substitution reflecting the curvature of the frontier. The relationship between the so-called FDEF approach and the cone-ratio model is explored in some detail. It is demonstrated that a decomposition of the facet generation process followed by the use of one of the available (exponential) convex hull algorithms allows for an explicit identification of the facial structure of the possibility set in fairly large DEA data sets. It is a main point to be made that the difficulties encountered for an identification of all facets in a DEA-possibility set can be circumvented in a number of empirical data sets and that this type of information can be used for a characterization of the structural properties of the frontier. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
  • Handle: RePEc:kap:jproda:v:20:y:2003:i:3:p:323-360
    DOI: 10.1023/A:1027303901017
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    References listed on IDEAS

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    1. Merja Halme & Tarja Joro & Pekka Korhonen & Seppo Salo & Jyrki Wallenius, 1999. "A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis," Management Science, INFORMS, vol. 45(1), pages 103-115, January.
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    Cited by:

    1. Amatatsu, Hirofumi & Ueda, Tohru, 2012. "Measurement of simultaneous scale and mix changes in inputs and outputs using DEA facets and RTS," European Journal of Operational Research, Elsevier, vol. 223(3), pages 752-761.
    2. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    3. repec:pal:jorsoc:v:68:y:2017:i:5:d:10.1057_s41274-016-0129-8 is not listed on IDEAS
    4. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    5. repec:eee:ejores:v:262:y:2017:i:2:p:792-801 is not listed on IDEAS
    6. Fukuyama, Hirofumi & Sekitani, Kazuyuki, 2012. "Decomposing the efficient frontier of the DEA production possibility set into a smallest number of convex polyhedrons by mixed integer programming," European Journal of Operational Research, Elsevier, vol. 221(1), pages 165-174.
    7. Hirofumi Fukuyama & Kazuyuki Sekitani, 2012. "An efficiency measure satisfying the Dmitruk–Koshevoy criteria on DEA technologies," Journal of Productivity Analysis, Springer, vol. 38(2), pages 131-143, October.
    8. Asmild, Mette & Hougaard, Jens Leth & Olesen, Ole B., 2013. "Testing over-representation of observations in subsets of a DEA technology," European Journal of Operational Research, Elsevier, vol. 230(1), pages 88-96.
    9. Mehdiloozad, Mahmood & Mirdehghan, S. Morteza & Sahoo, Biresh K. & Roshdi, Israfil, 2015. "On the identification of the global reference set in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(3), pages 779-788.
    10. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    11. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    12. Aparicio, Juan & Pastor, Jesús T. & Vidal, Fernando & Zofío, José L., 2017. "Evaluating productive performance: A new approach based on the product-mix problem consistent with Data Envelopment Analysis," Omega, Elsevier, vol. 67(C), pages 134-144.
    13. Bogetoft, Peter & Hougaard, Jens Leth & Smilgins, Aleksandrs, 2016. "Applied cost allocation: The DEA–Aumann–Shapley approach," European Journal of Operational Research, Elsevier, vol. 254(2), pages 667-678.
    14. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    15. Washio, Satoshi & Yamada, Syuuji & Tanaka, Tamaki & Tanino, Tetsuzo, 2012. "Improvements by analyzing the efficient frontier in DEA," European Journal of Operational Research, Elsevier, vol. 217(1), pages 173-184.
    16. Asmild, Mette & Zhu, Minyan, 2016. "Controlling for the use of extreme weights in bank efficiency assessments during the financial crisis," European Journal of Operational Research, Elsevier, vol. 251(3), pages 999-1015.
    17. Cooper, William W. & Ruiz, Jose L. & Sirvent, Inmaculada, 2007. "Choosing weights from alternative optimal solutions of dual multiplier models in DEA," European Journal of Operational Research, Elsevier, vol. 180(1), pages 443-458, July.
    18. Wei, Quanling & Yan, Hong & Xiong, Lin, 2008. "A bi-objective generalized data envelopment analysis model and point-to-set mapping projection," European Journal of Operational Research, Elsevier, vol. 190(3), pages 855-876, November.
    19. Ando, Kazutoshi & Minamide, Masato & Sekitani, Kazuyuki & Shi, Jianming, 2017. "Monotonicity of minimum distance inefficiency measures for Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 260(1), pages 232-243.

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